The thing which comes once in a year twice in a month 4 times in a week 6 times in a day?

A very badly mangled puzzle.

It usually depends on a precise formulation of the puzzle and tends to be the letter 'a' when asked like "What comes once in every year, but four times in an average day?"

So it is one A in 'every yeAr' and four A in 'An AvergAge dAy'.

Note that this should be phrased as 'every year', not 'a year' to work.